summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of (…

summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of ( f(x)=\frac{x + 2}{x - 2} ).\nfind the ( y )-intercepts of ( f(x) ). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the ( y )-intercept(s) is/are at ( y = - 1 ).\n(type an integer or a decimal. use a comma to separate answers as needed.)\nb. there are no ( y )-intercepts.\nfind any horizontal asymptotes of ( f(x) ). select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.\na. the function has one horizontal asymptote, .\n(type an equation.)\nb. the function has two horizontal asymptotes. the top asymptote is and the bottom asymptote is \n(type equations.)\nc. there are no horizontal asymptotes

summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of ( f(x)=\frac{x + 2}{x - 2} ).\nfind the ( y )-intercepts of ( f(x) ). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the ( y )-intercept(s) is/are at ( y = - 1 ).\n(type an integer or a decimal. use a comma to separate answers as needed.)\nb. there are no ( y )-intercepts.\nfind any horizontal asymptotes of ( f(x) ). select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.\na. the function has one horizontal asymptote, .\n(type an equation.)\nb. the function has two horizontal asymptotes. the top asymptote is and the bottom asymptote is \n(type equations.)\nc. there are no horizontal asymptotes

Answer

Explanation:

Step1: Find the y - intercept

The y - intercept is found by setting (x = 0) in the function (y=f(x)=\frac{x + 2}{x-2}). Substitute (x = 0) into the function: (y=\frac{0 + 2}{0-2}=\frac{2}{-2}=-1).

Step2: Find the horizontal asymptote

For a rational function (y=\frac{ax^{n}+...}{bx^{m}+...}), when (n=m) (here (n = m=1) for (y=\frac{x + 2}{x-2})), the horizontal asymptote is (y=\frac{a}{b}). Here (a = 1) (coefficient of (x) in the numerator) and (b = 1) (coefficient of (x) in the denominator), so (y=\frac{1}{1}=1).

Answer:

  • For the y - intercept: A. The y - intercept(s) is/are at (y=-1)
  • For the horizontal asymptote: A. The function has one horizontal asymptote, (y = 1)